This generally to adaptive optics wavefront control systems. More particularly, this invention relates to a new and improved Hartman wavefront tilt sensor having both very high sensitivity and wide dynamic range.
Optical wavefront sensors known as Hartmann sensors are well known in the art. An example of a Hartmann wavefront sensor is described in U.S. Pat. No. 4,141,652. This type of sensor is composed of an array of wavefront gradient (tilt) sensors and a reconstructor. The tilt magnitudes in X and Y directions are measured in each of a number of subapertures which are contiguous with no appreciable gaps existing between subapertures. By a process of two dimensional numerical integration, the tilt measurements may be combined to reconstruct a wavefront phase map in which high spatial frequencies are missing because of the smoothing action of averaging tilt over the area of each subaperture.
Referring herein to prior art FIG. 1, the Hartmann wavefront sensor described in U.S. Pat. No. 4,141,652 is shown generally at 10. An input optical beam 12 is roughly collimated and falls upon a lenslet array 14. The lenslet array is a closely packed, two dimensional array of lenses 16. Each lens 16 focuses a portion of the input beam (i.e., a subaperture beam) onto a two-dimensional array of position sensitive detectors 18. The detector array 18 can be formed by suitably mounting individual quadrant cell trackers, one for each lenslet (subaperture), or by a monolithic array of photosensitive pixels, such as are available in charge injection devices (CID) or charge coupled device (CCD) detector arrays.
The intensity of light falling on one sub-unit or pixel of the detector array 18 is read out in the form of an electronic charge or current into a centroid computer 20. After reading out the electronic signals (proportional to the light impinging on each pixel) corresponding to all the pixels in the array of detectors 18 into the centroid computer 20, the centroid computer calculates (through either analog or digital computing) the first moment of the intensity distribution in both X and Y directions for each subaperture. This is the intensity centroid and, if the lenslet arrays have reasonably good optical quality, is proportional to the input wavefront tilt averaged over the subaperture area of each lenslet 16.
A wavefront reconstructor 22 receives the X and Y centroid Positions for each subaperture which, when multiplied by a suitable conversion factor, represents the subaperture wavefront tilts. Reconstructor 22 can be analog in operation, such as an array of resistors driven by current sources for each tilt measurement. In this case, the wavefront phases can be recovered at the array of points between the subapertures by measuring the voltages present at the nodes of the resistor array. Another implementation is a digital computer which performs the numerical integration of the tilts by matrix multiplication to produce an array of input phase estimates.
Referring herein to prior art FIG. 2, in a typical closed-loop system for controlling the adaptive optics control loops, an input optical beam 24 is reflected off a deformable mirror 26 whose shape is controlled by a plurality of piston actuators 28. The light beam is then passed through a high-quality beam splitter 30 with negligible optical aberrations. A first portion 32 of the light is reflected by beam splitter 30 to form the compensated output optical beam 32. A second portion 34 of the light reflected by the deformable mirror 26 is transmitted by the beam splitter 30 to the wavefront sensor 10 (FIG. 1). The reconstructed wavefront phase deviations from the desired (planar) shape serve as error signals to identical negative-feedback servo control loops, one for each phase measurement point and its corresponding piston actuator 28 in the deformable mirror assembly. Servo electronics 36 receive the wavefront phase error signals, process them by multiplication and normally by integration and frequency-dependent filtering to achieve high gain and freedom from undesirable oscillations. Servo electronics 36 also drives the actuators 28 in the direction to reduce the wavefront phase errors. It will be appreciated that under steady state conditions, the surface of the deformable mirror 26 is driven to the conjugate of the input beam wavefront shape so that upon reflection, the light is equiphase across the beam both going onto the wavefront sensor 10 and also at the beam control system output 32.
A disadvantage of the two-dimensional detector array 18 is the large number of pixels required to achieve a useful dynamic range of input wavefront deviations from the nominal shape, which is usually taken as planar. That is, at least three, and normally four pixels are required to measure the X and Y centroid coordinates for each subaperture (and therefore the subaperture wavefront tilt). If sufficient sensitivity could be achieved with this minimum number of pixels, then the detector could be read out quickly in series with a fast response time. This is necessary to achieve a large temporal bandwidth when the wavefront sensor is used as part of an adaptive optics wavefront control system. For large subaperture tilts the spots may also overlap or appear so far from their nominal positions that either it is impossible to tell which spot belongs to which subaperture (in the case of a CID/CCD array); or the spot misses the detector altogether and no centroid determination is possible. On the other hand, if a very large tilt dynamic range is achieved by, for example, using a lenslet with a very short focal length, then noise sources such as shot noise, dark current, nonlinearity, charge transfer inefficiency, quantization, etc. will limit the precision with which the centroid can be determined even near the null operating point. In this case, the closed-loop operation may be limited by the lack of sensitivity, with the result being that the output beam has wavefront deviations due to noise sources internal to the wavefront sensor which are clearly undesirable.
For the closed-loop beam control system, the large capture range and the high sensitivity required in the subaperture tilt sensor can be achieved in several ways. One method is to use a larger number of pixels, arranged so that the spot diameter is larger than one pixel. This allows centroid determination to a small fraction of a pixel size. Using many such pixels (for example, an 8.times.8 array) will allow a large dynamic capture range for each spot without confusion. However, this method inevitably results in a reduced temporal bandwidth since many more pixels must now be read out which takes a correspondingly longer time period. Alternatively, many fewer subapertures could be sensed in the same time, but again this is highly undesirable since higher spatial frequency information about the wavefront shape will be lost. Thus, one must give up either high temporal bandwidth or high spatial frequency information with this method if the readout rate of array detectors is assumed to be constant.
The prior art has addressed this problem with a coarse/fine gradient sensor described in U.S. Pat. No. 4,950,878, assigned to the assignee hereof and incorporated herein by reference. Referring herein to prior art FIG. 3, the coarse/fine gradient sensor described in U.S. Pat. No. 4,950,878 is shown generally at 38. An input optical beam 40 is subdivided into ray bundles for each subaperture 42 and is passed to a beam splitter 44. Upon reflection, part of the light is focused by lenslet 46 with focal length f.sub.c upon a photosensitive quadrant cell 48 producing electronic signals on a line 50 used by a centroid computer 52 to calculate the X and Y coarse centroid position and to provide an electrical signal indicative thereof on a line 53. The other part of the subaperture light beam passing through beam splitter 44 is focused by a lenslet 54 of focal length f.sub.f to produce a spot on a quadrant cell 56 producing electronic signals 58 used by a centroid computer 60 to calculate the X and Y fine centroid position and to provide an electrical signal indicative thereof on a line 62. A centroid selector 64 selects as its output on a line 66 the coarse centroid signal from line 53 when the radial coarse centroid error is above a threshold value P. The centroid selector 64 selects the fine centroid signal from line 62 as its output when the coarse centroid signal is below the radial threshold value P.
The focal length f.sub.f is chosen to be much longer than f.sub.c so that the linear motion of the light spot on the quadrant cell is much greater for the fine channel (54, 56) than for the coarse channel (46, 48) given the same subaperture tilt of the input subaperture 42. Thus, the fine channel will have higher sensitivity but smaller dynamic range than the coarse channel.
During operation, the coarse channel quadrant cell dimensions and focal length f.sub.c are selected to provide sufficient tilt dynamic range for unambiguous tilt measurement, even if the quadrant cells are close together for neighboring subapertures. In the limit, adjacent blocks of four (4) pixels in a CID/CCD array may be used for the coarse channel sensing, and either another part of the same monolithic chip detector array or a second detector array could be used for the fine sensors.
The minimum practical number of pixels required for each subaperture is 8 (4 for coarse and 4 for fine). If each (synthesized) quadrant cell can be read out with sufficient precision to achieve a resolution of one part in R of the capture (maximum) centroid range, then the combined coarse/fine ranges multiply to produce a combined ratio of dynamic range to resolution of R.sup.2. In this case, the ratio of fine to coarse lenslet focal length is f.sub.f /f.sub.c =R. If each quadrant cell can be used to determine the centroid to B binary bits of precision (where B is approximately equal to log.sub.2 R), then the coarse/fine combination has a precision of 2B binary bits [=log.sub.2 (R.sup.2)]. This is a much more efficient usage of pixels than can be achieved by grouping more than four into a single centroid sensor. For instance, with 8 pixels rather than 4, dynamic range is only increased in each dimension by roughly (8/4).sup.1/2 =(2)h. Thus, increasing the number of pixels used in a single centroid sensor only increases the relative precision by the square root of the ratio of the numbers of pixels. By creating new centroid sensors, the improvement in relative precision is much greater if successively greater sensitivities are used for each centroid sensor.
As mentioned, a longer focal length lenslet may be used to increase the sensitivity of the fine sensor. This could be accomplished in other ways such as using a smaller diameter pixel sensor and a correspondingly smaller beamlet spot size.
The minimum spot size S for a collimated input beam generated by a distant point source is EQU S=2.44.lambda.f/d
where .lambda. is the wavelength, d is the lenslet aperture, and f is the lenslet focal length. For spatially extended sources of the input beam, it may be desirable to spatially place the photosensitive detector away from the lens focus so as to produce a larger, defocused spot. By doing this, the size of the spot depends less on the angular size of the light source and therefore, the calibration of the centroid detector will suffer smaller errors due to variable source size.
While the coarse/fine gradient sensor of U.S. Pat. No. 4,950,878 provides a significant improvement in sensitivity and dynamic range over the prior art, a need exists to simplify such adaptive optics wavefront control systems.